Analysis of 111/999 NHS calls and 111 online reports
Quentin Leclerc, Emily Nightingale, Samuel Abbott & Thibaut Jombart, for CMMID
Monday 08 June 2020
1 Data preparation
1.1 Outline
Load scripts: loads libraries and useful scripts used in the analyses; all
.Rfiles contained inscriptsat the root of the factory are automatically loadedLoad data: imports datasets, and may contain some ad hoc changes to the data such as specific data cleaning (not used in other reports), new variables used in the analyses, etc.
1.2 Load packages
library(reportfactory)
library(here)
library(rio)
library(tidyverse)
library(incidence)
library(distcrete)
library(epitrix)
library(earlyR)
library(projections)
library(linelist)
library(remotes)
library(janitor)
library(kableExtra)
library(DT)
library(cyphr)
library(chngpt)
library(lubridate)
library(ggpubr)
library(ggnewscale)1.3 Load scripts
These scripts will load:
- all scripts stored as
.Rfiles inside/scripts/ - all scripts stored as
.Rfiles inside/src/
These scripts also contain routines to access the latest clean encrypted data (see next section).
1.4 Load clean data
We import the latest NHS pathways data:
x <- import_pathways() %>%
as_tibble()
x
## [90m# A tibble: 137,634 x 11[39m
## site_type date sex age ccg_code ccg_name count postcode nhs_region
## [3m[90m<chr>[39m[23m [3m[90m<date>[39m[23m [3m[90m<chr>[39m[23m [3m[90m<chr>[39m[23m [3m[90m<chr>[39m[23m [3m[90m<chr>[39m[23m [3m[90m<int>[39m[23m [3m[90m<chr>[39m[23m [3m[90m<chr>[39m[23m
## [90m 1[39m 111 2020-03-18 fema… 0-18 e380000… nhs_bar… 35 rm13ae London
## [90m 2[39m 111 2020-03-18 fema… 0-18 e380000… nhs_bed… 27 mk454hr East of E…
## [90m 3[39m 111 2020-03-18 fema… 0-18 e380000… nhs_bla… 9 bb12fd North West
## [90m 4[39m 111 2020-03-18 fema… 0-18 e380000… nhs_bro… 11 br33ql London
## [90m 5[39m 111 2020-03-18 fema… 0-18 e380000… nhs_can… 9 ws111jp Midlands
## [90m 6[39m 111 2020-03-18 fema… 0-18 e380000… nhs_cit… 12 n15lz London
## [90m 7[39m 111 2020-03-18 fema… 0-18 e380000… nhs_enf… 7 en40dy London
## [90m 8[39m 111 2020-03-18 fema… 0-18 e380000… nhs_ham… 6 dl62uu North Eas…
## [90m 9[39m 111 2020-03-18 fema… 0-18 e380000… nhs_har… 24 ts232la North Eas…
## [90m10[39m 111 2020-03-18 fema… 0-18 e380000… nhs_kin… 6 kt11eu London
## [90m# … with 137,624 more rows, and 2 more variables: day [3m[90m<int>[90m[23m, weekday [3m[90m<fct>[90m[23m[39mWe also import demographics data for NHS regions in England, used later in our analysis:
path <- here::here("data", "csv", "nhs_region_population_2018.csv")
nhs_region_pop <- rio::import(path) %>%
mutate(nhs_region = str_to_title(gsub("_"," ",nhs_region)))
nhs_region_pop$nhs_region <- gsub(" Of ", " of ", nhs_region_pop$nhs_region)
nhs_region_pop$nhs_region <- gsub(" And ", " and ", nhs_region_pop$nhs_region)
nhs_region_pop
## nhs_region variable value
## 1 North West 0-18 0.22538599
## 2 North East and Yorkshire 0-18 0.21876449
## 3 Midlands 0-18 0.22564656
## 4 East of England 0-18 0.22810783
## 5 London 0-18 0.23764782
## 6 South East 0-18 0.22458811
## 7 South West 0-18 0.20799797
## 8 North West 19-69 0.64274078
## 9 North East and Yorkshire 19-69 0.64437753
## 10 Midlands 19-69 0.63876675
## 11 East of England 19-69 0.63034229
## 12 London 19-69 0.67820084
## 13 South East 19-69 0.63267336
## 14 South West 19-69 0.63176131
## 15 North West 70-120 0.13187323
## 16 North East and Yorkshire 70-120 0.13685797
## 17 Midlands 70-120 0.13558669
## 18 East of England 70-120 0.14154988
## 19 London 70-120 0.08415135
## 20 South East 70-120 0.14273853
## 21 South West 70-120 0.16024072Finally, we import publically available deaths per NHS region:
dth <- import_deaths() %>%
mutate(nhs_region = str_to_title(gsub("_"," ",nhs_region)))
#truncation to account for reporting delay
delay_max <- 21
dth$nhs_region <- gsub(" Of ", " of ", dth$nhs_region)
dth$nhs_region <- gsub(" And ", " and ", dth$nhs_region)
dth
## date_report nhs_region deaths
## 1 2020-03-01 East of England 0
## 2 2020-03-02 East of England 1
## 3 2020-03-03 East of England 0
## 4 2020-03-04 East of England 0
## 5 2020-03-05 East of England 0
## 6 2020-03-06 East of England 1
## 7 2020-03-07 East of England 0
## 8 2020-03-08 East of England 0
## 9 2020-03-09 East of England 1
## 10 2020-03-10 East of England 0
## 11 2020-03-11 East of England 0
## 12 2020-03-12 East of England 0
## 13 2020-03-13 East of England 1
## 14 2020-03-14 East of England 2
## 15 2020-03-15 East of England 2
## 16 2020-03-16 East of England 1
## 17 2020-03-17 East of England 1
## 18 2020-03-18 East of England 5
## 19 2020-03-19 East of England 4
## 20 2020-03-20 East of England 2
## 21 2020-03-21 East of England 11
## 22 2020-03-22 East of England 12
## 23 2020-03-23 East of England 11
## 24 2020-03-24 East of England 19
## 25 2020-03-25 East of England 26
## 26 2020-03-26 East of England 36
## 27 2020-03-27 East of England 38
## 28 2020-03-28 East of England 28
## 29 2020-03-29 East of England 43
## 30 2020-03-30 East of England 45
## 31 2020-03-31 East of England 70
## 32 2020-04-01 East of England 61
## 33 2020-04-02 East of England 64
## 34 2020-04-03 East of England 80
## 35 2020-04-04 East of England 71
## 36 2020-04-05 East of England 76
## 37 2020-04-06 East of England 71
## 38 2020-04-07 East of England 93
## 39 2020-04-08 East of England 111
## 40 2020-04-09 East of England 87
## 41 2020-04-10 East of England 74
## 42 2020-04-11 East of England 91
## 43 2020-04-12 East of England 101
## 44 2020-04-13 East of England 78
## 45 2020-04-14 East of England 61
## 46 2020-04-15 East of England 82
## 47 2020-04-16 East of England 74
## 48 2020-04-17 East of England 86
## 49 2020-04-18 East of England 64
## 50 2020-04-19 East of England 67
## 51 2020-04-20 East of England 67
## 52 2020-04-21 East of England 75
## 53 2020-04-22 East of England 67
## 54 2020-04-23 East of England 49
## 55 2020-04-24 East of England 66
## 56 2020-04-25 East of England 54
## 57 2020-04-26 East of England 48
## 58 2020-04-27 East of England 46
## 59 2020-04-28 East of England 58
## 60 2020-04-29 East of England 32
## 61 2020-04-30 East of England 44
## 62 2020-05-01 East of England 49
## 63 2020-05-02 East of England 29
## 64 2020-05-03 East of England 41
## 65 2020-05-04 East of England 19
## 66 2020-05-05 East of England 35
## 67 2020-05-06 East of England 30
## 68 2020-05-07 East of England 33
## 69 2020-05-08 East of England 33
## 70 2020-05-09 East of England 29
## 71 2020-05-10 East of England 22
## 72 2020-05-11 East of England 18
## 73 2020-05-12 East of England 21
## 74 2020-05-13 East of England 27
## 75 2020-05-14 East of England 26
## 76 2020-05-15 East of England 19
## 77 2020-05-16 East of England 26
## 78 2020-05-17 East of England 17
## 79 2020-05-18 East of England 24
## 80 2020-05-19 East of England 15
## 81 2020-05-20 East of England 26
## 82 2020-05-21 East of England 21
## 83 2020-05-22 East of England 13
## 84 2020-05-23 East of England 12
## 85 2020-05-24 East of England 16
## 86 2020-05-25 East of England 25
## 87 2020-05-26 East of England 14
## 88 2020-05-27 East of England 12
## 89 2020-05-28 East of England 17
## 90 2020-05-29 East of England 15
## 91 2020-05-30 East of England 9
## 92 2020-05-31 East of England 8
## 93 2020-06-01 East of England 14
## 94 2020-06-02 East of England 12
## 95 2020-06-03 East of England 7
## 96 2020-06-04 East of England 4
## 97 2020-06-05 East of England 4
## 98 2020-06-06 East of England 1
## 99 2020-03-01 London 0
## 100 2020-03-02 London 0
## 101 2020-03-03 London 0
## 102 2020-03-04 London 0
## 103 2020-03-05 London 0
## 104 2020-03-06 London 1
## 105 2020-03-07 London 1
## 106 2020-03-08 London 0
## 107 2020-03-09 London 1
## 108 2020-03-10 London 0
## 109 2020-03-11 London 7
## 110 2020-03-12 London 6
## 111 2020-03-13 London 10
## 112 2020-03-14 London 14
## 113 2020-03-15 London 10
## 114 2020-03-16 London 17
## 115 2020-03-17 London 25
## 116 2020-03-18 London 31
## 117 2020-03-19 London 25
## 118 2020-03-20 London 45
## 119 2020-03-21 London 50
## 120 2020-03-22 London 54
## 121 2020-03-23 London 64
## 122 2020-03-24 London 87
## 123 2020-03-25 London 113
## 124 2020-03-26 London 130
## 125 2020-03-27 London 130
## 126 2020-03-28 London 122
## 127 2020-03-29 London 147
## 128 2020-03-30 London 150
## 129 2020-03-31 London 181
## 130 2020-04-01 London 202
## 131 2020-04-02 London 190
## 132 2020-04-03 London 196
## 133 2020-04-04 London 230
## 134 2020-04-05 London 195
## 135 2020-04-06 London 198
## 136 2020-04-07 London 219
## 137 2020-04-08 London 238
## 138 2020-04-09 London 205
## 139 2020-04-10 London 170
## 140 2020-04-11 London 176
## 141 2020-04-12 London 158
## 142 2020-04-13 London 166
## 143 2020-04-14 London 143
## 144 2020-04-15 London 142
## 145 2020-04-16 London 139
## 146 2020-04-17 London 99
## 147 2020-04-18 London 101
## 148 2020-04-19 London 102
## 149 2020-04-20 London 95
## 150 2020-04-21 London 95
## 151 2020-04-22 London 108
## 152 2020-04-23 London 77
## 153 2020-04-24 London 71
## 154 2020-04-25 London 57
## 155 2020-04-26 London 53
## 156 2020-04-27 London 51
## 157 2020-04-28 London 43
## 158 2020-04-29 London 44
## 159 2020-04-30 London 39
## 160 2020-05-01 London 41
## 161 2020-05-02 London 40
## 162 2020-05-03 London 36
## 163 2020-05-04 London 29
## 164 2020-05-05 London 25
## 165 2020-05-06 London 36
## 166 2020-05-07 London 37
## 167 2020-05-08 London 29
## 168 2020-05-09 London 23
## 169 2020-05-10 London 26
## 170 2020-05-11 London 18
## 171 2020-05-12 London 18
## 172 2020-05-13 London 16
## 173 2020-05-14 London 20
## 174 2020-05-15 London 18
## 175 2020-05-16 London 14
## 176 2020-05-17 London 15
## 177 2020-05-18 London 9
## 178 2020-05-19 London 13
## 179 2020-05-20 London 19
## 180 2020-05-21 London 12
## 181 2020-05-22 London 10
## 182 2020-05-23 London 6
## 183 2020-05-24 London 7
## 184 2020-05-25 London 8
## 185 2020-05-26 London 12
## 186 2020-05-27 London 7
## 187 2020-05-28 London 7
## 188 2020-05-29 London 7
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## 190 2020-05-31 London 6
## 191 2020-06-01 London 8
## 192 2020-06-02 London 6
## 193 2020-06-03 London 5
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## 195 2020-06-05 London 2
## 196 2020-06-06 London 0
## 197 2020-03-01 Midlands 0
## 198 2020-03-02 Midlands 0
## 199 2020-03-03 Midlands 1
## 200 2020-03-04 Midlands 0
## 201 2020-03-05 Midlands 0
## 202 2020-03-06 Midlands 0
## 203 2020-03-07 Midlands 0
## 204 2020-03-08 Midlands 3
## 205 2020-03-09 Midlands 1
## 206 2020-03-10 Midlands 0
## 207 2020-03-11 Midlands 2
## 208 2020-03-12 Midlands 6
## 209 2020-03-13 Midlands 5
## 210 2020-03-14 Midlands 4
## 211 2020-03-15 Midlands 5
## 212 2020-03-16 Midlands 11
## 213 2020-03-17 Midlands 8
## 214 2020-03-18 Midlands 13
## 215 2020-03-19 Midlands 8
## 216 2020-03-20 Midlands 28
## 217 2020-03-21 Midlands 13
## 218 2020-03-22 Midlands 31
## 219 2020-03-23 Midlands 33
## 220 2020-03-24 Midlands 41
## 221 2020-03-25 Midlands 48
## 222 2020-03-26 Midlands 64
## 223 2020-03-27 Midlands 72
## 224 2020-03-28 Midlands 89
## 225 2020-03-29 Midlands 92
## 226 2020-03-30 Midlands 90
## 227 2020-03-31 Midlands 123
## 228 2020-04-01 Midlands 140
## 229 2020-04-02 Midlands 142
## 230 2020-04-03 Midlands 124
## 231 2020-04-04 Midlands 151
## 232 2020-04-05 Midlands 164
## 233 2020-04-06 Midlands 140
## 234 2020-04-07 Midlands 123
## 235 2020-04-08 Midlands 186
## 236 2020-04-09 Midlands 139
## 237 2020-04-10 Midlands 127
## 238 2020-04-11 Midlands 142
## 239 2020-04-12 Midlands 139
## 240 2020-04-13 Midlands 120
## 241 2020-04-14 Midlands 116
## 242 2020-04-15 Midlands 147
## 243 2020-04-16 Midlands 102
## 244 2020-04-17 Midlands 118
## 245 2020-04-18 Midlands 115
## 246 2020-04-19 Midlands 92
## 247 2020-04-20 Midlands 107
## 248 2020-04-21 Midlands 86
## 249 2020-04-22 Midlands 78
## 250 2020-04-23 Midlands 103
## 251 2020-04-24 Midlands 79
## 252 2020-04-25 Midlands 72
## 253 2020-04-26 Midlands 81
## 254 2020-04-27 Midlands 74
## 255 2020-04-28 Midlands 68
## 256 2020-04-29 Midlands 53
## 257 2020-04-30 Midlands 56
## 258 2020-05-01 Midlands 64
## 259 2020-05-02 Midlands 51
## 260 2020-05-03 Midlands 52
## 261 2020-05-04 Midlands 61
## 262 2020-05-05 Midlands 58
## 263 2020-05-06 Midlands 59
## 264 2020-05-07 Midlands 48
## 265 2020-05-08 Midlands 34
## 266 2020-05-09 Midlands 37
## 267 2020-05-10 Midlands 41
## 268 2020-05-11 Midlands 33
## 269 2020-05-12 Midlands 45
## 270 2020-05-13 Midlands 39
## 271 2020-05-14 Midlands 36
## 272 2020-05-15 Midlands 40
## 273 2020-05-16 Midlands 34
## 274 2020-05-17 Midlands 31
## 275 2020-05-18 Midlands 34
## 276 2020-05-19 Midlands 34
## 277 2020-05-20 Midlands 36
## 278 2020-05-21 Midlands 32
## 279 2020-05-22 Midlands 26
## 280 2020-05-23 Midlands 31
## 281 2020-05-24 Midlands 19
## 282 2020-05-25 Midlands 25
## 283 2020-05-26 Midlands 32
## 284 2020-05-27 Midlands 29
## 285 2020-05-28 Midlands 27
## 286 2020-05-29 Midlands 20
## 287 2020-05-30 Midlands 20
## 288 2020-05-31 Midlands 20
## 289 2020-06-01 Midlands 20
## 290 2020-06-02 Midlands 20
## 291 2020-06-03 Midlands 21
## 292 2020-06-04 Midlands 11
## 293 2020-06-05 Midlands 13
## 294 2020-06-06 Midlands 2
## 295 2020-03-01 North East and Yorkshire 0
## 296 2020-03-02 North East and Yorkshire 0
## 297 2020-03-03 North East and Yorkshire 0
## 298 2020-03-04 North East and Yorkshire 0
## 299 2020-03-05 North East and Yorkshire 0
## 300 2020-03-06 North East and Yorkshire 0
## 301 2020-03-07 North East and Yorkshire 0
## 302 2020-03-08 North East and Yorkshire 0
## 303 2020-03-09 North East and Yorkshire 0
## 304 2020-03-10 North East and Yorkshire 0
## 305 2020-03-11 North East and Yorkshire 0
## 306 2020-03-12 North East and Yorkshire 0
## 307 2020-03-13 North East and Yorkshire 0
## 308 2020-03-14 North East and Yorkshire 0
## 309 2020-03-15 North East and Yorkshire 2
## 310 2020-03-16 North East and Yorkshire 3
## 311 2020-03-17 North East and Yorkshire 1
## 312 2020-03-18 North East and Yorkshire 2
## 313 2020-03-19 North East and Yorkshire 6
## 314 2020-03-20 North East and Yorkshire 5
## 315 2020-03-21 North East and Yorkshire 6
## 316 2020-03-22 North East and Yorkshire 7
## 317 2020-03-23 North East and Yorkshire 9
## 318 2020-03-24 North East and Yorkshire 8
## 319 2020-03-25 North East and Yorkshire 18
## 320 2020-03-26 North East and Yorkshire 21
## 321 2020-03-27 North East and Yorkshire 28
## 322 2020-03-28 North East and Yorkshire 35
## 323 2020-03-29 North East and Yorkshire 38
## 324 2020-03-30 North East and Yorkshire 64
## 325 2020-03-31 North East and Yorkshire 60
## 326 2020-04-01 North East and Yorkshire 67
## 327 2020-04-02 North East and Yorkshire 74
## 328 2020-04-03 North East and Yorkshire 100
## 329 2020-04-04 North East and Yorkshire 105
## 330 2020-04-05 North East and Yorkshire 92
## 331 2020-04-06 North East and Yorkshire 96
## 332 2020-04-07 North East and Yorkshire 102
## 333 2020-04-08 North East and Yorkshire 107
## 334 2020-04-09 North East and Yorkshire 111
## 335 2020-04-10 North East and Yorkshire 117
## 336 2020-04-11 North East and Yorkshire 98
## 337 2020-04-12 North East and Yorkshire 84
## 338 2020-04-13 North East and Yorkshire 94
## 339 2020-04-14 North East and Yorkshire 107
## 340 2020-04-15 North East and Yorkshire 96
## 341 2020-04-16 North East and Yorkshire 103
## 342 2020-04-17 North East and Yorkshire 88
## 343 2020-04-18 North East and Yorkshire 95
## 344 2020-04-19 North East and Yorkshire 88
## 345 2020-04-20 North East and Yorkshire 100
## 346 2020-04-21 North East and Yorkshire 76
## 347 2020-04-22 North East and Yorkshire 84
## 348 2020-04-23 North East and Yorkshire 62
## 349 2020-04-24 North East and Yorkshire 72
## 350 2020-04-25 North East and Yorkshire 69
## 351 2020-04-26 North East and Yorkshire 65
## 352 2020-04-27 North East and Yorkshire 65
## 353 2020-04-28 North East and Yorkshire 57
## 354 2020-04-29 North East and Yorkshire 69
## 355 2020-04-30 North East and Yorkshire 57
## 356 2020-05-01 North East and Yorkshire 64
## 357 2020-05-02 North East and Yorkshire 48
## 358 2020-05-03 North East and Yorkshire 40
## 359 2020-05-04 North East and Yorkshire 49
## 360 2020-05-05 North East and Yorkshire 40
## 361 2020-05-06 North East and Yorkshire 50
## 362 2020-05-07 North East and Yorkshire 45
## 363 2020-05-08 North East and Yorkshire 42
## 364 2020-05-09 North East and Yorkshire 44
## 365 2020-05-10 North East and Yorkshire 40
## 366 2020-05-11 North East and Yorkshire 29
## 367 2020-05-12 North East and Yorkshire 27
## 368 2020-05-13 North East and Yorkshire 28
## 369 2020-05-14 North East and Yorkshire 30
## 370 2020-05-15 North East and Yorkshire 32
## 371 2020-05-16 North East and Yorkshire 35
## 372 2020-05-17 North East and Yorkshire 26
## 373 2020-05-18 North East and Yorkshire 29
## 374 2020-05-19 North East and Yorkshire 27
## 375 2020-05-20 North East and Yorkshire 21
## 376 2020-05-21 North East and Yorkshire 33
## 377 2020-05-22 North East and Yorkshire 22
## 378 2020-05-23 North East and Yorkshire 18
## 379 2020-05-24 North East and Yorkshire 23
## 380 2020-05-25 North East and Yorkshire 21
## 381 2020-05-26 North East and Yorkshire 21
## 382 2020-05-27 North East and Yorkshire 18
## 383 2020-05-28 North East and Yorkshire 19
## 384 2020-05-29 North East and Yorkshire 24
## 385 2020-05-30 North East and Yorkshire 20
## 386 2020-05-31 North East and Yorkshire 18
## 387 2020-06-01 North East and Yorkshire 15
## 388 2020-06-02 North East and Yorkshire 22
## 389 2020-06-03 North East and Yorkshire 21
## 390 2020-06-04 North East and Yorkshire 15
## 391 2020-06-05 North East and Yorkshire 12
## 392 2020-06-06 North East and Yorkshire 11
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## 406 2020-03-14 North West 1
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## 409 2020-03-17 North West 4
## 410 2020-03-18 North West 6
## 411 2020-03-19 North West 7
## 412 2020-03-20 North West 10
## 413 2020-03-21 North West 11
## 414 2020-03-22 North West 13
## 415 2020-03-23 North West 16
## 416 2020-03-24 North West 21
## 417 2020-03-25 North West 21
## 418 2020-03-26 North West 29
## 419 2020-03-27 North West 35
## 420 2020-03-28 North West 28
## 421 2020-03-29 North West 46
## 422 2020-03-30 North West 67
## 423 2020-03-31 North West 52
## 424 2020-04-01 North West 86
## 425 2020-04-02 North West 96
## 426 2020-04-03 North West 95
## 427 2020-04-04 North West 98
## 428 2020-04-05 North West 102
## 429 2020-04-06 North West 100
## 430 2020-04-07 North West 133
## 431 2020-04-08 North West 127
## 432 2020-04-09 North West 119
## 433 2020-04-10 North West 117
## 434 2020-04-11 North West 138
## 435 2020-04-12 North West 126
## 436 2020-04-13 North West 127
## 437 2020-04-14 North West 131
## 438 2020-04-15 North West 114
## 439 2020-04-16 North West 134
## 440 2020-04-17 North West 98
## 441 2020-04-18 North West 113
## 442 2020-04-19 North West 71
## 443 2020-04-20 North West 83
## 444 2020-04-21 North West 76
## 445 2020-04-22 North West 86
## 446 2020-04-23 North West 85
## 447 2020-04-24 North West 66
## 448 2020-04-25 North West 65
## 449 2020-04-26 North West 55
## 450 2020-04-27 North West 54
## 451 2020-04-28 North West 57
## 452 2020-04-29 North West 62
## 453 2020-04-30 North West 59
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## 455 2020-05-02 North West 56
## 456 2020-05-03 North West 55
## 457 2020-05-04 North West 48
## 458 2020-05-05 North West 48
## 459 2020-05-06 North West 44
## 460 2020-05-07 North West 49
## 461 2020-05-08 North West 42
## 462 2020-05-09 North West 30
## 463 2020-05-10 North West 41
## 464 2020-05-11 North West 34
## 465 2020-05-12 North West 38
## 466 2020-05-13 North West 24
## 467 2020-05-14 North West 26
## 468 2020-05-15 North West 33
## 469 2020-05-16 North West 32
## 470 2020-05-17 North West 24
## 471 2020-05-18 North West 30
## 472 2020-05-19 North West 35
## 473 2020-05-20 North West 25
## 474 2020-05-21 North West 25
## 475 2020-05-22 North West 26
## 476 2020-05-23 North West 31
## 477 2020-05-24 North West 26
## 478 2020-05-25 North West 31
## 479 2020-05-26 North West 27
## 480 2020-05-27 North West 27
## 481 2020-05-28 North West 27
## 482 2020-05-29 North West 19
## 483 2020-05-30 North West 17
## 484 2020-05-31 North West 13
## 485 2020-06-01 North West 12
## 486 2020-06-02 North West 25
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## 523 2020-04-02 South East 55
## 524 2020-04-03 South East 72
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## 531 2020-04-10 South East 88
## 532 2020-04-11 South East 88
## 533 2020-04-12 South East 88
## 534 2020-04-13 South East 84
## 535 2020-04-14 South East 65
## 536 2020-04-15 South East 72
## 537 2020-04-16 South East 56
## 538 2020-04-17 South East 86
## 539 2020-04-18 South East 57
## 540 2020-04-19 South East 70
## 541 2020-04-20 South East 85
## 542 2020-04-21 South East 50
## 543 2020-04-22 South East 54
## 544 2020-04-23 South East 57
## 545 2020-04-24 South East 64
## 546 2020-04-25 South East 51
## 547 2020-04-26 South East 51
## 548 2020-04-27 South East 40
## 549 2020-04-28 South East 40
## 550 2020-04-29 South East 47
## 551 2020-04-30 South East 29
## 552 2020-05-01 South East 37
## 553 2020-05-02 South East 36
## 554 2020-05-03 South East 17
## 555 2020-05-04 South East 35
## 556 2020-05-05 South East 29
## 557 2020-05-06 South East 25
## 558 2020-05-07 South East 27
## 559 2020-05-08 South East 26
## 560 2020-05-09 South East 28
## 561 2020-05-10 South East 19
## 562 2020-05-11 South East 25
## 563 2020-05-12 South East 27
## 564 2020-05-13 South East 18
## 565 2020-05-14 South East 32
## 566 2020-05-15 South East 24
## 567 2020-05-16 South East 22
## 568 2020-05-17 South East 17
## 569 2020-05-18 South East 22
## 570 2020-05-19 South East 12
## 571 2020-05-20 South East 22
## 572 2020-05-21 South East 14
## 573 2020-05-22 South East 17
## 574 2020-05-23 South East 19
## 575 2020-05-24 South East 16
## 576 2020-05-25 South East 13
## 577 2020-05-26 South East 17
## 578 2020-05-27 South East 17
## 579 2020-05-28 South East 12
## 580 2020-05-29 South East 17
## 581 2020-05-30 South East 8
## 582 2020-05-31 South East 10
## 583 2020-06-01 South East 11
## 584 2020-06-02 South East 9
## 585 2020-06-03 South East 15
## 586 2020-06-04 South East 8
## 587 2020-06-05 South East 6
## 588 2020-06-06 South East 0
## 589 2020-03-01 South West 0
## 590 2020-03-02 South West 0
## 591 2020-03-03 South West 0
## 592 2020-03-04 South West 0
## 593 2020-03-05 South West 0
## 594 2020-03-06 South West 0
## 595 2020-03-07 South West 0
## 596 2020-03-08 South West 0
## 597 2020-03-09 South West 0
## 598 2020-03-10 South West 0
## 599 2020-03-11 South West 1
## 600 2020-03-12 South West 0
## 601 2020-03-13 South West 0
## 602 2020-03-14 South West 1
## 603 2020-03-15 South West 0
## 604 2020-03-16 South West 0
## 605 2020-03-17 South West 2
## 606 2020-03-18 South West 2
## 607 2020-03-19 South West 5
## 608 2020-03-20 South West 3
## 609 2020-03-21 South West 6
## 610 2020-03-22 South West 9
## 611 2020-03-23 South West 9
## 612 2020-03-24 South West 7
## 613 2020-03-25 South West 9
## 614 2020-03-26 South West 11
## 615 2020-03-27 South West 13
## 616 2020-03-28 South West 21
## 617 2020-03-29 South West 18
## 618 2020-03-30 South West 23
## 619 2020-03-31 South West 23
## 620 2020-04-01 South West 22
## 621 2020-04-02 South West 23
## 622 2020-04-03 South West 30
## 623 2020-04-04 South West 42
## 624 2020-04-05 South West 32
## 625 2020-04-06 South West 34
## 626 2020-04-07 South West 39
## 627 2020-04-08 South West 47
## 628 2020-04-09 South West 24
## 629 2020-04-10 South West 46
## 630 2020-04-11 South West 43
## 631 2020-04-12 South West 23
## 632 2020-04-13 South West 27
## 633 2020-04-14 South West 24
## 634 2020-04-15 South West 32
## 635 2020-04-16 South West 29
## 636 2020-04-17 South West 33
## 637 2020-04-18 South West 25
## 638 2020-04-19 South West 31
## 639 2020-04-20 South West 26
## 640 2020-04-21 South West 26
## 641 2020-04-22 South West 22
## 642 2020-04-23 South West 17
## 643 2020-04-24 South West 19
## 644 2020-04-25 South West 15
## 645 2020-04-26 South West 27
## 646 2020-04-27 South West 13
## 647 2020-04-28 South West 17
## 648 2020-04-29 South West 15
## 649 2020-04-30 South West 26
## 650 2020-05-01 South West 6
## 651 2020-05-02 South West 7
## 652 2020-05-03 South West 10
## 653 2020-05-04 South West 16
## 654 2020-05-05 South West 14
## 655 2020-05-06 South West 18
## 656 2020-05-07 South West 16
## 657 2020-05-08 South West 6
## 658 2020-05-09 South West 11
## 659 2020-05-10 South West 5
## 660 2020-05-11 South West 8
## 661 2020-05-12 South West 7
## 662 2020-05-13 South West 7
## 663 2020-05-14 South West 6
## 664 2020-05-15 South West 4
## 665 2020-05-16 South West 4
## 666 2020-05-17 South West 6
## 667 2020-05-18 South West 4
## 668 2020-05-19 South West 6
## 669 2020-05-20 South West 1
## 670 2020-05-21 South West 9
## 671 2020-05-22 South West 6
## 672 2020-05-23 South West 6
## 673 2020-05-24 South West 3
## 674 2020-05-25 South West 8
## 675 2020-05-26 South West 11
## 676 2020-05-27 South West 5
## 677 2020-05-28 South West 9
## 678 2020-05-29 South West 4
## 679 2020-05-30 South West 3
## 680 2020-05-31 South West 2
## 681 2020-06-01 South West 6
## 682 2020-06-02 South West 2
## 683 2020-06-03 South West 5
## 684 2020-06-04 South West 1
## 685 2020-06-05 South West 1
## 686 2020-06-06 South West 01.5 Completion date
We extract the completion date from the NHS Pathways file timestamp:
The completion date of the NHS Pathways data is Sunday 07 Jun 2020.
1.6 Auxiliary functions
These are functions which will be used further in the analyses.
Function to estimate the generalised R-squared as the proportion of deviance explained by a given model:
## Function to calculate R2 for Poisson model
## not adjusted for model complexity but all models have the same DF here
Rsq <- function(x) {
1 - (x$deviance / x$null.deviance)
}Function to extract growth rates per region as well as halving times, and the associated 95% confidence intervals:
## function to extract the coefficients, find the level of the intercept,
## reconstruct the values of r, get confidence intervals
get_r <- function(model) {
## extract coefficients and conf int
out <- data.frame(r = coef(model)) %>%
rownames_to_column("var") %>%
cbind(confint(model)) %>%
filter(!grepl("day_of_week", var)) %>%
filter(grepl("day", var)) %>%
rename(lower_95 = "2.5 %",
upper_95 = "97.5 %") %>%
mutate(var = sub("day:", "", var))
## reconstruct values: intercept + region-coefficient
for (i in 2:nrow(out)) {
out[i, -1] <- out[1, -1] + out[i, -1]
}
## find the name of the intercept, restore regions names
out <- out %>%
mutate(nhs_region = model$xlevels$nhs_region) %>%
select(nhs_region, everything(), -var)
## find halving times
halving <- log(0.5) / out[,-1] %>%
rename(halving_t = r,
halving_t_lower_95 = lower_95,
halving_t_upper_95 = upper_95)
## set halving times with exclusion intervals to NA
no_halving <- out$lower_95 < 0 & out$upper_95 > 0
halving[no_halving, ] <- NA_real_
## return all data
cbind(out, halving)
}Functions used in the correlation analysis between NHS Pathways reports and deaths:
## Function to calculate Pearson's correlation between deaths and lagged
## reports. Note that `pearson` can be replaced with `spearman` for rank
## correlation.
getcor <- function(x, ndx) {
return(cor(x$deaths[ndx],
x$note_lag[ndx],
use = "complete.obs",
method = "pearson"))
}
## Catch if sample size throws an error
getcor2 <- possibly(getcor, otherwise = NA)
getboot <- function(x) {
result <- boot::boot.ci(boot::boot(x, getcor2, R = 1000),
type = "bca")
return(data.frame(n = sum(!is.na(x$note_lag) & !is.na(x$deaths)),
r = result$t0,
r_low = result$bca[4],
r_hi = result$bca[5]))
}Function to classify the day of the week into weekend, Monday, and the rest:
## Fn to add day of week
day_of_week <- function(df) {
df %>%
dplyr::mutate(day_of_week = lubridate::wday(date, label = TRUE)) %>%
dplyr::mutate(day_of_week = dplyr::case_when(
day_of_week %in% c("Sat", "Sun") ~ "weekend",
day_of_week %in% c("Mon") ~ "monday",
!(day_of_week %in% c("Sat", "Sun", "Mon")) ~ "rest_of_week"
) %>%
factor(levels = c("rest_of_week", "monday", "weekend")))
}Custom color palettes, color scales, and vectors of colors:
2 Temporal trends in NHS Pathways reports
2.1 Outline
We look for temporal patterns in COVID-19 related 111/999 calls and 111 online reports. Analyses are broken down by NHS region. We also look for estimates of recent growth rate and associated doubling / halving time.
2.2 Reports by region over time
tab_date_region_all <- x %>%
filter(!is.na(nhs_region)) %>%
group_by(date, nhs_region) %>%
summarise(n = sum(count))
dth %>%
mutate(trusted = case_when(date_report < max(dth$date_report)-delay_max ~ "Y",
date_report >= max(dth$date_report)-delay_max ~ "N"),
value = "Deaths",
vline = max(dth$date_report)-delay_max-1,
lab = "Truncated for reporting delay",
lab_pos_x = vline + 10,
lab_pos_y = 150,
lab_col = "darkgrey") %>%
rename(date = date_report,
n = deaths) %>%
bind_rows(
mutate(tab_date_region_all, value = "Reports",
trusted = "Y",
vline = as.Date("2020-03-23"),
lab = "Start of UK lockdown",
lab_pos_x = vline - 8,
lab_pos_y = 30200,
lab_col = "black")
) %>%
mutate(value = factor(value, levels = c("Reports","Deaths"))) -> dths_reports
plot_dth_report <-
ggplot(dths_reports, aes(date, n, colour = nhs_region)) +
# Add main points and lines, coloured by region and fade out deaths for excluded period
geom_point(aes(alpha = trusted)) +
geom_line(alpha = 0.2) +
geom_smooth(method = "loess", span = .5, color = "black") +
scale_colour_manual("", values = pal) +
scale_alpha_manual(values = c(0.3,1)) +
guides(alpha = F) +
# Add vertical markers for important dates with labels - different for each facet
ggnewscale::new_scale_colour() +
geom_vline(aes(xintercept = vline, col = value), lty = "solid") +
geom_text(aes(x = lab_pos_x, y = lab_pos_y, label = lab, col = value), size = 3) +
scale_colour_manual("",values = c("black","darkgrey"), guide = F) +
# Facet by deaths and reports
facet_grid(rows = vars(value), scales = "free_y", switch = "y") +
# Other formatting
theme_bw() +
scale_weeks +
theme(legend.position = "bottom",strip.placement = "outside") +
rotate_x +
labs(x = NULL,
y = NULL)
plot_dth_report
2.3 Reports by region by age over time
We plot the number of 111/999 calls and 111 online reports by age, and the proportion of 111/999 calls and 111 online reports by age. In the second graph, the vertical lines indicate the proportion of individuals residing in the corresponding NHS region who belong to the corresponding age group.
tab_date_region_age_all <- x %>%
filter(!is.na(nhs_region),
age != "missing") %>%
group_by(date, nhs_region, age) %>%
summarise(n = sum(count))
tab_date_region_age_all %>%
ggplot(aes(x = date, y = n, fill = age)) +
geom_col(position = "stack") +
scale_fill_manual(values = age.pal) +
theme_bw() +
scale_weeks +
theme(legend.position = "bottom",
axis.text.x = element_text(angle = 90, hjust = 1)) +
guides(fill = guide_legend(title = "Age", ncol = 3)) +
labs(x = NULL,
y = "Total daily reports by age") +
facet_wrap(~ nhs_region, ncol = 4)
tab_date_region_age_all <- tab_date_region_age_all %>%
group_by(date, nhs_region) %>%
summarise(tot = sum(n)) %>%
left_join(tab_date_region_age_all, by = c("date", "nhs_region")) %>%
mutate(prop_n = n/tot)
tab_date_region_age_all %>%
ggplot(aes(x = date, y = prop_n, color = age)) +
scale_color_manual(values = age.pal) +
geom_line() +
geom_point() +
geom_hline(data = nhs_region_pop, aes(yintercept = value, color = variable)) +
theme_bw() +
scale_weeks +
theme(legend.position = "bottom",
axis.text.x = element_text(angle = 90, hjust = 1)) +
guides(color = guide_legend(title = "Age", ncol = 3)) +
labs(x = NULL,
y = "Proportion of daily reports by age") +
facet_wrap(~ nhs_region, ncol = 4)
2.4 Moving window model
We fit quasi-Poisson GLMs for 14-day windows to get growth rates over time.
## set moving time window (1/2/3 weeks)
w <- 14
# create empty df
r_all_sliding <- NULL
## make data for model
x_model_all_moving <- x %>%
filter(!is.na(nhs_region)) %>%
group_by(date, nhs_region) %>%
summarise(n = sum(count))
unique_dates <- unique(x_model_all_moving$date)
for (i in 1:(length(unique_dates) - w)) {
date_i <- unique_dates[i]
date_i_max <- date_i + w
model_data <- x_model_all_moving %>%
filter(date >= date_i & date < date_i_max) %>%
mutate(day = as.integer(date - date_i)) %>%
day_of_week()
mod <- glm(n ~ day * nhs_region + day_of_week,
data = model_data,
family = 'quasipoisson')
# get growth rate
r <- get_r(mod)
r$w_min <- date_i
r$w_max <- date_i_max
# combine all estimates
r_all_sliding <- bind_rows(r_all_sliding, r)
}
#serial interval distribution
SI_param = epitrix::gamma_mucv2shapescale(4.7, 2.9/4.7)
SI_distribution <- distcrete::distcrete("gamma", interval = 1,
shape = SI_param$shape,
scale = SI_param$scale,
w = 0.5)
#convert growth rates r to R0
r_all_sliding <- r_all_sliding %>%
mutate(R = epitrix::r2R0(r, SI_distribution),
R_lower_95 = epitrix::r2R0(lower_95, SI_distribution),
R_upper_95 = epitrix::r2R0(upper_95, SI_distribution))We examine the evolution of the growth rate by region over time.
# plot
plot_growth <-
r_all_sliding %>%
ggplot(aes(x = w_max, y = r)) +
geom_ribbon(aes(ymin = lower_95, ymax = upper_95, fill = nhs_region), alpha = 0.1) +
geom_line(aes(colour = nhs_region)) +
geom_point(aes(colour = nhs_region)) +
geom_hline(yintercept = 0, linetype = "dashed") +
theme_bw() +
scale_weeks +
theme(legend.position = "bottom",
plot.margin = margin(0.5,1,0.5,0.5, "cm")) +
guides(colour = guide_legend(title = "", override.aes = list(fill = NA)), fill = FALSE) +
labs(x = "",
y = "Estimated daily growth rate (r)") +
scale_colour_manual(values = pal)From the growth rate, we derive R and examine its value through time.
# plot
plot_R <-
r_all_sliding %>%
ggplot(aes(x = w_max, y = R)) +
geom_ribbon(aes(ymin = R_lower_95, ymax = R_upper_95, fill = nhs_region), alpha = 0.1) +
geom_line(aes(colour = nhs_region)) +
geom_point(aes(colour = nhs_region)) +
geom_hline(yintercept = 1, linetype = "dashed") +
theme_bw() +
scale_weeks +
theme(legend.position = "bottom",
plot.margin = margin(0.5,1,0.5,0.5, "cm")) +
guides(color = guide_legend(title = "", override.aes = list(fill = NA)), fill = FALSE) +
labs(x = "",
y = "Estimated effective reproduction\nnumber (Re)") +
scale_colour_manual(values = pal)
R <- r_all_sliding %>%
mutate(lower_95 = R_lower_95,
upper_95 = R_upper_95,
value = R,
measure = "R",
reference = 1)
r_R <- r_all_sliding %>%
mutate(measure = "r",
value = r,
reference = 0) %>%
bind_rows(R)
r_R %>%
ggplot(aes(x = w_max, y = value)) +
geom_ribbon(aes(ymin = lower_95, ymax = upper_95, fill = nhs_region), alpha = 0.1) +
geom_line(aes(colour = nhs_region)) +
geom_point(aes(colour = nhs_region)) +
geom_hline(aes(yintercept = reference), linetype = "dashed") +
theme_bw() +
scale_weeks +
rotate_x +
theme(legend.position = "bottom",
plot.margin = margin(0.5,1,0,0, "cm"),
strip.background = element_blank(),
# strip.text.x = element_blank(),
strip.placement = "outside"
) +
guides(color = guide_legend(title = "",
override.aes = list(fill = NA)),
fill = FALSE) +
labs(x = "", y = "") +
scale_colour_manual(values = pal) +
facet_grid(rows = vars(measure),
scales = "free_y",
switch = "y",
labeller = as_labeller(c(r = "Daily growth rate (r)",
R = "Effective reproduction\nnumber (Re)")))
2.5 Moving window model - stratified by age
We repeat the above analysis, where we fit quasi-Poisson GLMs for 14-day windows to get growth rates over time, but apply this to each age group separately (0-18, 19-69, 70-120 years old).
We first run the analysis for 0-18 years old.
## set moving time window (2 weeks)
w <- 14
# create empty df
r_all_sliding_0_18 <- NULL
## make data for model
x_model_all_moving_0_18 <- x %>%
filter(!is.na(nhs_region),
age == "0-18") %>%
group_by(date, nhs_region) %>%
summarise(n = sum(count))
unique_dates <- unique(x_model_all_moving_0_18$date)
for (i in 1:(length(unique_dates) - w)) {
date_i <- unique_dates[i]
date_i_max <- date_i + w
model_data <- x_model_all_moving_0_18 %>%
filter(date >= date_i & date < date_i_max) %>%
mutate(day = as.integer(date - date_i)) %>%
day_of_week()
mod <- glm(n ~ day * nhs_region + day_of_week,
data = model_data,
family = 'quasipoisson')
# get growth rate
r <- get_r(mod)
r$w_min <- date_i
r$w_max <- date_i_max
# combine all estimates
r_all_sliding_0_18 <- bind_rows(r_all_sliding_0_18, r)
}
#serial interval distribution
SI_param = epitrix::gamma_mucv2shapescale(4.7, 2.9/4.7)
SI_distribution <- distcrete::distcrete("gamma", interval = 1,
shape = SI_param$shape,
scale = SI_param$scale, w = 0.5)
#convert growth rates r to R0
r_all_sliding_0_18 <- r_all_sliding_0_18 %>%
mutate(R = epitrix::r2R0(r, SI_distribution),
R_lower_95 = epitrix::r2R0(lower_95, SI_distribution),
R_upper_95 = epitrix::r2R0(upper_95, SI_distribution))# plot
plot_growth <-
r_all_sliding_0_18 %>%
ggplot(aes(x = w_max, y = r)) +
geom_ribbon(aes(ymin = lower_95, ymax = upper_95, fill = nhs_region), alpha = 0.1) +
geom_line(aes(colour = nhs_region)) +
geom_point(aes(colour = nhs_region)) +
geom_hline(yintercept = 0, linetype = "dashed") +
theme_bw() +
scale_weeks +
theme(legend.position = "bottom",
plot.margin = margin(0.5,1,0.5,0.5, "cm")) +
guides(colour = guide_legend(title = "",override.aes = list(fill = NA)), fill = FALSE) +
labs(x = "",
y = "Estimated daily growth rate (r)"
) +
scale_colour_manual(values = pal)# plot
plot_R <-
r_all_sliding_0_18 %>%
ggplot(aes(x = w_max, y = R)) +
geom_ribbon(aes(ymin = R_lower_95, ymax = R_upper_95, fill = nhs_region), alpha = 0.1) +
geom_line(aes(colour = nhs_region)) +
geom_point(aes(colour = nhs_region)) +
geom_hline(yintercept = 1, linetype = "dashed") +
theme_bw() +
scale_weeks +
theme(legend.position = "bottom",
plot.margin = margin(0.5,1,0.5,0.5, "cm")) +
guides(color = guide_legend(title = "", override.aes = list(fill = NA)), fill = FALSE) +
labs(x = "",
y = "Estimated effective reproduction\nnumber (Re)"
) +
scale_colour_manual(values = pal)
R <- r_all_sliding_0_18 %>%
mutate(lower_95 = R_lower_95,
upper_95 = R_upper_95,
value = R,
measure = "R",
reference = 1)
r_R <- r_all_sliding_0_18 %>%
mutate(measure = "r",
value = r,
reference = 0) %>%
bind_rows(R)
fig2_3_0_18 <- r_R %>%
ggplot(aes(x = w_max, y = value)) +
geom_ribbon(aes(ymin = lower_95, ymax = upper_95, fill = nhs_region), alpha = 0.1) +
geom_line(aes(colour = nhs_region)) +
geom_point(aes(colour = nhs_region)) +
geom_hline(aes(yintercept = reference), linetype = "dashed") +
theme_bw() +
scale_weeks +
theme(legend.position = "bottom",
plot.margin = margin(0.5,1,0,0, "cm"),
strip.background = element_blank(),
strip.placement = "outside"
) +
guides(color = guide_legend(title = "", override.aes = list(fill = NA)), fill = FALSE) +
labs(x = "", y = "") +
scale_colour_manual(values = pal) +
facet_grid(rows = vars(measure),
scales = "free_y",
switch = "y",
labeller = as_labeller(c(r = "Daily growth rate (r)",
R = "Effective reproduction\nnumber (Re)")))Then, we run the analysis for 19-69 years old.
## set moving time window (2 weeks)
w <- 14
# create empty df
r_all_sliding_19_69 <- NULL
## make data for model
x_model_all_moving_19_69 <- x %>%
filter(!is.na(nhs_region),
age == "19-69") %>%
group_by(date, nhs_region) %>%
summarise(n = sum(count))
unique_dates <- unique(x_model_all_moving_19_69$date)
for (i in 1:(length(unique_dates) - w)) {
date_i <- unique_dates[i]
date_i_max <- date_i + w
model_data <- x_model_all_moving_19_69 %>%
filter(date >= date_i & date < date_i_max) %>%
mutate(day = as.integer(date - date_i)) %>%
day_of_week()
mod <- glm(n ~ day * nhs_region + day_of_week,
data = model_data,
family = 'quasipoisson')
# get growth rate
r <- get_r(mod)
r$w_min <- date_i
r$w_max <- date_i_max
# combine all estimates
r_all_sliding_19_69 <- bind_rows(r_all_sliding_19_69, r)
}
#serial interval distribution
SI_param = epitrix::gamma_mucv2shapescale(4.7, 2.9/4.7)
SI_distribution <- distcrete::distcrete("gamma", interval = 1,
shape = SI_param$shape,
scale = SI_param$scale, w = 0.5)
#convert growth rates r to R0
r_all_sliding_19_69 <- r_all_sliding_19_69 %>%
mutate(R = epitrix::r2R0(r, SI_distribution),
R_lower_95 = epitrix::r2R0(lower_95, SI_distribution),
R_upper_95 = epitrix::r2R0(upper_95, SI_distribution))# plot
plot_growth <-
r_all_sliding_19_69 %>%
ggplot(aes(x = w_max, y = r)) +
geom_ribbon(aes(ymin = lower_95, ymax = upper_95, fill = nhs_region), alpha = 0.1) +
geom_line(aes(colour = nhs_region)) +
geom_point(aes(colour = nhs_region)) +
geom_hline(yintercept = 0, linetype = "dashed") +
theme_bw() +
scale_weeks +
theme(legend.position = "bottom",
plot.margin = margin(0.5,1,0.5,0.5, "cm")) +
guides(colour = guide_legend(title = "", override.aes = list(fill = NA)), fill = FALSE) +
labs(x = "",
y = "Estimated daily growth rate (r)") +
scale_colour_manual(values = pal)# plot
plot_R <-
r_all_sliding_19_69 %>%
ggplot(aes(x = w_max, y = R)) +
geom_ribbon(aes(ymin = R_lower_95, ymax = R_upper_95, fill = nhs_region), alpha = 0.1) +
geom_line(aes(colour = nhs_region)) +
geom_point(aes(colour = nhs_region)) +
geom_hline(yintercept = 1, linetype = "dashed") +
theme_bw() +
scale_weeks +
theme(legend.position = "bottom",
plot.margin = margin(0.5,1,0.5,0.5, "cm")) +
guides(color = guide_legend(title = "", override.aes = list(fill = NA)), fill = FALSE) +
labs(x = "",
y = "Estimated effective reproduction\nnumber (Re)"
) +
scale_colour_manual(values = pal)
R <- r_all_sliding_19_69 %>%
mutate(lower_95 = R_lower_95,
upper_95 = R_upper_95,
value = R,
measure = "R",
reference = 1)
r_R <- r_all_sliding_19_69 %>%
mutate(measure = "r",
value = r,
reference = 0) %>%
bind_rows(R)
fig2_3_19_69 <- r_R %>%
ggplot(aes(x = w_max, y = value)) +
geom_ribbon(aes(ymin = lower_95, ymax = upper_95, fill = nhs_region), alpha = 0.1) +
geom_line(aes(colour = nhs_region)) +
geom_point(aes(colour = nhs_region)) +
geom_hline(aes(yintercept = reference), linetype = "dashed") +
theme_bw() +
scale_weeks +
theme(legend.position = "bottom",
plot.margin = margin(0.5,1,0,0, "cm"),
strip.background = element_blank(),
strip.placement = "outside"
) +
guides(color = guide_legend(title = "", override.aes = list(fill = NA)), fill = FALSE) +
labs(x = "", y = "") +
scale_colour_manual(values = pal) +
facet_grid(rows = vars(measure),
scales = "free_y",
switch = "y",
labeller = as_labeller(c(r = "Daily growth rate (r)",
R = "Effective reproduction\nnumber (Re)")))Finally, we run the analysis for 70-120 years old.
## set moving time window (2 weeks)
w <- 14
# create empty df
r_all_sliding_70_120 <- NULL
## make data for model
x_model_all_moving_70_120 <- x %>%
filter(!is.na(nhs_region),
age == "70-120") %>%
group_by(date, nhs_region) %>%
summarise(n = sum(count))
unique_dates <- unique(x_model_all_moving_70_120$date)
for (i in 1:(length(unique_dates) - w)) {
date_i <- unique_dates[i]
date_i_max <- date_i + w
model_data <- x_model_all_moving_70_120 %>%
filter(date >= date_i & date < date_i_max) %>%
mutate(day = as.integer(date - date_i)) %>%
day_of_week()
mod <- glm(n ~ day * nhs_region + day_of_week,
data = model_data,
family = 'quasipoisson')
# get growth rate
r <- get_r(mod)
r$w_min <- date_i
r$w_max <- date_i_max
# combine all estimates
r_all_sliding_70_120 <- bind_rows(r_all_sliding_70_120, r)
}
#serial interval distribution
SI_param = epitrix::gamma_mucv2shapescale(4.7, 2.9/4.7)
SI_distribution <- distcrete::distcrete("gamma", interval = 1,
shape = SI_param$shape,
scale = SI_param$scale, w = 0.5)
#convert growth rates r to R0
r_all_sliding_70_120 <- r_all_sliding_70_120 %>%
mutate(R = epitrix::r2R0(r, SI_distribution),
R_lower_95 = epitrix::r2R0(lower_95, SI_distribution),
R_upper_95 = epitrix::r2R0(upper_95, SI_distribution))# plot
plot_growth <-
r_all_sliding_70_120 %>%
ggplot(aes(x = w_max, y = r)) +
geom_ribbon(aes(ymin = lower_95, ymax = upper_95, fill = nhs_region), alpha = 0.1) +
geom_line(aes(colour = nhs_region)) +
geom_point(aes(colour = nhs_region)) +
geom_hline(yintercept = 0, linetype = "dashed") +
theme_bw() +
scale_weeks +
theme(legend.position = "bottom",
plot.margin = margin(0.5,1,0.5,0.5, "cm")) +
guides(colour = guide_legend(title = "",override.aes = list(fill = NA)), fill = FALSE) +
labs(x = "",
y = "Estimated daily growth rate (r)"
) +
scale_colour_manual(values = pal)# plot
plot_R <-
r_all_sliding_70_120 %>%
ggplot(aes(x = w_max, y = R)) +
geom_ribbon(aes(ymin = R_lower_95, ymax = R_upper_95, fill = nhs_region), alpha = 0.1) +
geom_line(aes(colour = nhs_region)) +
geom_point(aes(colour = nhs_region)) +
geom_hline(yintercept = 1, linetype = "dashed") +
theme_bw() +
scale_weeks +
theme(legend.position = "bottom",
plot.margin = margin(0.5,1,0.5,0.5, "cm")) +
guides(color = guide_legend(title = "", override.aes = list(fill = NA)), fill = FALSE) +
labs(x = "",
y = "Estimated effective reproduction\nnumber (Re)") +
scale_colour_manual(values = pal)
R <- r_all_sliding_70_120 %>%
mutate(lower_95 = R_lower_95,
upper_95 = R_upper_95,
value = R,
measure = "R",
reference = 1)
r_R <- r_all_sliding_70_120 %>%
mutate(measure = "r",
value = r,
reference = 0) %>%
bind_rows(R)
fig2_3_70_120 <- r_R %>%
ggplot(aes(x = w_max, y = value)) +
geom_ribbon(aes(ymin = lower_95, ymax = upper_95, fill = nhs_region), alpha = 0.1) +
geom_line(aes(colour = nhs_region)) +
geom_point(aes(colour = nhs_region)) +
geom_hline(aes(yintercept = reference), linetype = "dashed") +
theme_bw() +
scale_weeks +
theme(legend.position = "bottom",
plot.margin = margin(0.5,1,0,0, "cm"),
strip.background = element_blank(),
strip.placement = "outside"
) +
guides(color = guide_legend(title = "", override.aes = list(fill = NA)), fill = FALSE) +
labs(x = "", y = "") +
scale_colour_manual(values = pal) +
facet_grid(rows = vars(measure),
scales = "free_y",
switch = "y",
labeller = as_labeller(c(r = "Daily growth rate (r)",
R = "Effective reproduction\nnumber (Re)"))) We combine the estimated growth rates and effective reproduction numbers into a single figure.
ggpubr::ggarrange(fig2_3_0_18,
fig2_3_19_69,
fig2_3_70_120,
nrow = 3,
labels = "AUTO",
common.legend = TRUE,
legend = "bottom",
align = "hv") 
3 Comparison with deaths time series
3.1 Outline
We want to explore the correlation between NHS Pathways reports and deaths, and assess the potential for reports to be used as an early warning system for disease resurgence.
Death data are publically available. We truncate the time series to avoid bias from reporting delay - we assume a conservative delay of three weeks.
3.2 Lagged correlation
We calculate Pearson’s correlation coefficient between deaths and NHS Pathways notifications using different lags. Confidence intervals are obtained using bootstrap. Note that results were also confirmed using Spearman’s rank correlation.
First we join the NHS Pathways and death data, and aggregate over all England:
## truncate death data for reporting delay
trunc_date <- max(dth$date_report) - delay_max
dth_trunc <- dth %>%
rename(date = date_report) %>%
filter(date <= trunc_date)
## join with notification data
all_data <- x %>%
filter(!is.na(nhs_region)) %>%
group_by(date, nhs_region) %>%
summarise(count = sum(count, na.rm = T)) %>%
ungroup %>%
inner_join(dth_trunc,
by = c("date","nhs_region"))
all_tot <- all_data %>%
group_by(date) %>%
summarise(count = sum(count, na.rm = TRUE),
deaths = sum(deaths, na.rm = TRUE)) We calculate correlation with lagged NHS Pathways reports from 0 to 30 days behind deaths:
## Calculate all correlations + bootstrap CIs
lag_cor <- data.frame()
for (i in 0:30) {
## lag reports
summary <- all_tot %>%
mutate(note_lag = lag(count, i)) %>%
## calculate rank correlation and bootstrap CI
getboot(.) %>%
mutate(lag = i)
lag_cor <- bind_rows(lag_cor, summary)
}
cor_vs_lag <- ggplot(lag_cor, aes(lag, r)) +
theme_bw() +
geom_ribbon(aes(ymin = r_low, ymax = r_hi), alpha = 0.2) +
geom_hline(yintercept = 0, lty = "longdash") +
geom_point() +
geom_line() +
labs(x = "Lag between NHS pathways and death data (days)",
y = "Pearson's correlation") +
large_txt
cor_vs_lag
This analysis suggests that the best lag is 23 days. We then compare and plot the number of deaths reported against the number of NHS Pathways reports lagged by 23 days.
all_tot <- all_tot %>%
rename(date_death = date) %>%
mutate(note_lag = lag(count, lag_cor$lag[l_opt]),
note_lag_c = (note_lag - mean(note_lag, na.rm = T)),
date_note = lag(date_death,16))
lag_mod <- glm(deaths ~ note_lag, data = all_tot, family = "quasipoisson")
summary(lag_mod)
##
## Call:
## glm(formula = deaths ~ note_lag, family = "quasipoisson", data = all_tot)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -7.6046 -1.9041 0.3866 1.7380 4.5943
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 5.127e+00 5.061e-02 101.31 <2e-16 ***
## note_lag 1.016e-05 4.834e-07 21.02 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for quasipoisson family taken to be 7.090473)
##
## Null deviance: 3409.25 on 36 degrees of freedom
## Residual deviance: 254.21 on 35 degrees of freedom
## (23 observations deleted due to missingness)
## AIC: NA
##
## Number of Fisher Scoring iterations: 4
exp(coefficients(lag_mod))
## (Intercept) note_lag
## 168.54197 1.00001
exp(confint(lag_mod))
## 2.5 % 97.5 %
## (Intercept) 152.484417 185.946533
## note_lag 1.000009 1.000011
Rsq(lag_mod)
## [1] 0.9254348
mod_fit <- as.data.frame(predict(lag_mod, type = "link", se.fit = TRUE)[1:2])
all_tot_pred <-
all_tot %>%
filter(!is.na(note_lag)) %>%
mutate(pred = mod_fit$fit,
pred.se = mod_fit$se.fit,
low = exp(pred - 1.96*pred.se),
hi = exp(pred + 1.96*pred.se))
glm_fit <- all_tot_pred %>%
filter(!is.na(note_lag)) %>%
ggplot(aes(x = note_lag, y = deaths)) +
geom_point() +
geom_line(aes(y = exp(pred))) +
geom_ribbon(aes(ymin = low, ymax = hi), alpha = 0.3, col = "grey") +
theme_bw() +
labs(y = "Daily number of\ndeaths reported",
x = "Daily number of NHS Pathways reports") +
large_txt
glm_fit
4 Supplementary figures
4.1 Serial interval distribution
This is a comparison of gamma versus lognormal distribution for the serial interval used to convert r to R in our analysis. Both distributions are parameterised with mean 4.7 and standard deviation 2.9.
SI_param <- epitrix::gamma_mucv2shapescale(4.7, 2.9/4.7)
SI_distribution <- distcrete::distcrete("gamma", interval = 1,
shape = SI_param$shape,
scale = SI_param$scale, w = 0.5)
SI_distribution2 <- distcrete::distcrete("lnorm", interval = 1,
meanlog = log(4.7),
sdlog = log(2.9), w = 0.5)
SI_dist1 <- data.frame(x = SI_distribution$r(1e5))
SI_dist1 <- count(SI_dist1, x) %>%
ggplot() +
geom_col(aes(x = x, y = n)) +
labs(x = "Serial interval (days)", y = "Frequency") +
scale_x_continuous(breaks = seq(0, 30, 5)) +
theme_bw()
SI_dist2 <- data.frame(x = SI_distribution2$r(1e5))
SI_dist2 <- count(SI_dist2, x) %>%
ggplot() +
geom_col(aes(x = x, y = n)) +
labs(x = "Serial interval (days)", y = "Frequency") +
scale_x_continuous(breaks = seq(0, 200, 20), limits = c(0, 200)) +
theme_bw()
ggpubr::ggarrange(SI_dist1,
SI_dist2,
nrow = 1,
labels = "AUTO") 
4.2 Sensitivity analysis - 7 or 21 days moving window
We reproduce the window analysis with either a 7 or 21 days window for sensitivity purposes.
First with the 7 days window:
## set moving time window (1/2/3 weeks)
w <- 7
# create empty df
r_all_sliding_7days <- NULL
## make data for model
x_model_all_moving <- x %>%
filter(!is.na(nhs_region)) %>%
group_by(date, nhs_region) %>%
summarise(n = sum(count))
unique_dates <- unique(x_model_all_moving$date)
for (i in 1:(length(unique_dates) - w)) {
date_i <- unique_dates[i]
date_i_max <- date_i + w
model_data <- x_model_all_moving %>%
filter(date >= date_i & date < date_i_max) %>%
mutate(day = as.integer(date - date_i)) %>%
day_of_week()
mod <- glm(n ~ day * nhs_region + day_of_week,
data = model_data,
family = 'quasipoisson')
# get growth rate
r <- get_r(mod)
r$w_min <- date_i
r$w_max <- date_i_max
# combine all estimates
r_all_sliding_7days <- bind_rows(r_all_sliding_7days, r)
}
#serial interval distribution
SI_param = epitrix::gamma_mucv2shapescale(4.7, 2.9/4.7)
SI_distribution <- distcrete::distcrete("gamma", interval = 1,
shape = SI_param$shape,
scale = SI_param$scale,
w = 0.5)
#convert growth rates r to R0
r_all_sliding_7days <- r_all_sliding_7days %>%
mutate(R = epitrix::r2R0(r, SI_distribution),
R_lower_95 = epitrix::r2R0(lower_95, SI_distribution),
R_upper_95 = epitrix::r2R0(upper_95, SI_distribution))# plot
plot_growth <-
r_all_sliding_7days %>%
ggplot(aes(x = w_max, y = r)) +
geom_ribbon(aes(ymin = lower_95, ymax = upper_95, fill = nhs_region), alpha = 0.1) +
geom_line(aes(colour = nhs_region)) +
geom_point(aes(colour = nhs_region)) +
geom_hline(yintercept = 0, linetype = "dashed") +
theme_bw() +
scale_weeks +
theme(legend.position = "bottom",
plot.margin = margin(0.5,1,0.5,0.5, "cm")) +
guides(colour = guide_legend(title = "",override.aes = list(fill = NA)), fill = FALSE) +
labs(x = "",
y = "Estimated daily growth rate (r)") +
scale_colour_manual(values = pal)plot_R <- r_all_sliding_7days %>%
ggplot(aes(x = w_max, y = R)) +
geom_ribbon(aes(ymin = R_lower_95, ymax = R_upper_95, fill = nhs_region), alpha = 0.1) +
geom_line(aes(colour = nhs_region)) +
geom_point(aes(colour = nhs_region)) +
geom_hline(yintercept = 1, linetype = "dashed") +
theme_bw() +
scale_weeks +
theme(legend.position = "bottom",
plot.margin = margin(0.5,1,0.5,0.5, "cm")) +
guides(color = guide_legend(title = "", override.aes = list(fill = NA)), fill = FALSE) +
labs(x = "",
y = "Estimated effective reproduction\nnumber (Re)") +
scale_colour_manual(values = pal)
R <- r_all_sliding_7days %>%
mutate(lower_95 = R_lower_95,
upper_95 = R_upper_95,
value = R,
measure = "R",
reference = 1)
r_R <- r_all_sliding_7days %>%
mutate(measure = "r",
value = r,
reference = 0) %>%
bind_rows(R)
r_R_7 <- r_R %>%
ggplot(aes(x = w_max, y = value)) +
geom_ribbon(aes(ymin = lower_95, ymax = upper_95, fill = nhs_region), alpha = 0.1) +
geom_line(aes(colour = nhs_region)) +
geom_point(aes(colour = nhs_region)) +
geom_hline(aes(yintercept = reference), linetype = "dashed") +
theme_bw() +
scale_weeks +
theme(legend.position = "bottom",
plot.margin = margin(0.5,1,0,0, "cm"),
strip.background = element_blank(),
strip.placement = "outside"
) +
guides(color = guide_legend(title = "", override.aes = list(fill = NA)), fill = FALSE) +
labs(x = "", y = "") +
scale_colour_manual(values = pal) +
facet_grid(rows = vars(measure),
scales = "free_y",
switch = "y",
labeller = as_labeller(c(r = "Daily growth rate (r)",
R = "Effective reproduction\nnumber (Re)")))Then with the 21 days window:
## set moving time window (1/2/3 weeks)
w <- 21
# create empty df
r_all_sliding_21days <- NULL
## make data for model
x_model_all_moving <- x %>%
filter(!is.na(nhs_region)) %>%
group_by(date, nhs_region) %>%
summarise(n = sum(count))
unique_dates <- unique(x_model_all_moving$date)
for (i in 1:(length(unique_dates) - w)) {
date_i <- unique_dates[i]
date_i_max <- date_i + w
model_data <- x_model_all_moving %>%
filter(date >= date_i & date < date_i_max) %>%
mutate(day = as.integer(date - date_i)) %>%
day_of_week()
mod <- glm(n ~ day * nhs_region + day_of_week,
data = model_data,
family = 'quasipoisson')
# get growth rate
r <- get_r(mod)
r$w_min <- date_i
r$w_max <- date_i_max
# combine all estimates
r_all_sliding_21days <- bind_rows(r_all_sliding_21days, r)
}
#serial interval distribution
SI_param = epitrix::gamma_mucv2shapescale(4.7, 2.9/4.7)
SI_distribution <- distcrete::distcrete("gamma", interval = 1,
shape = SI_param$shape,
scale = SI_param$scale,
w = 0.5)
#convert growth rates r to R0
r_all_sliding_21days <- r_all_sliding_21days %>%
mutate(R = epitrix::r2R0(r, SI_distribution),
R_lower_95 = epitrix::r2R0(lower_95, SI_distribution),
R_upper_95 = epitrix::r2R0(upper_95, SI_distribution))# plot
plot_growth <-
r_all_sliding_21days %>%
ggplot(aes(x = w_max, y = r)) +
geom_ribbon(aes(ymin = lower_95, ymax = upper_95, fill = nhs_region), alpha = 0.1) +
geom_line(aes(colour = nhs_region)) +
geom_point(aes(colour = nhs_region)) +
geom_hline(yintercept = 0, linetype = "dashed") +
theme_bw() +
scale_weeks +
theme(legend.position = "bottom",
plot.margin = margin(0.5,1,0.5,0.5, "cm")) +
guides(colour = guide_legend(title = "",override.aes = list(fill = NA)), fill = FALSE) +
labs(x = "",
y = "Estimated daily growth rate (r)") +
scale_colour_manual(values = pal)# plot
plot_R <-
r_all_sliding_21days %>%
ggplot(aes(x = w_max, y = R)) +
geom_ribbon(aes(ymin = R_lower_95, ymax = R_upper_95, fill = nhs_region), alpha = 0.1) +
geom_line(aes(colour = nhs_region)) +
geom_point(aes(colour = nhs_region)) +
geom_hline(yintercept = 1, linetype = "dashed") +
theme_bw() +
scale_weeks +
theme(legend.position = "bottom",
plot.margin = margin(0.5,1,0.5,0.5, "cm")) +
guides(color = guide_legend(title = "", override.aes = list(fill = NA)), fill = FALSE) +
labs(x = "",
y = "Estimated effective reproduction\nnumber (Re)") +
scale_colour_manual(values = pal)
R <- r_all_sliding_21days %>%
mutate(lower_95 = R_lower_95,
upper_95 = R_upper_95,
value = R,
measure = "R",
reference = 1)
r_R <- r_all_sliding_21days %>%
mutate(measure = "r",
value = r,
reference = 0) %>%
bind_rows(R)
r_R_21 <- r_R %>%
ggplot(aes(x = w_max, y = value)) +
geom_ribbon(aes(ymin = lower_95, ymax = upper_95, fill = nhs_region), alpha = 0.1) +
geom_line(aes(colour = nhs_region)) +
geom_point(aes(colour = nhs_region)) +
geom_hline(aes(yintercept = reference), linetype = "dashed") +
theme_bw() +
scale_weeks +
theme(legend.position = "bottom",
plot.margin = margin(0.5,1,0,0, "cm"),
strip.background = element_blank(),
strip.placement = "outside"
) +
guides(color = guide_legend(title = "", override.aes = list(fill = NA)), fill = FALSE) +
labs(x = "", y = "") +
scale_colour_manual(values = pal) +
facet_grid(rows = vars(measure),
scales = "free_y",
switch = "y",
labeller = as_labeller(c(r = "Daily growth rate (r)",
R = "Effective reproduction\nnumber (Re)")))And we combine both outputs into a single plot:
ggpubr::ggarrange(r_R_7,
r_R_21,
nrow = 2,
labels = "AUTO",
common.legend = TRUE,
legend = "bottom") 
4.3 Correlation between NHS Pathways reports and deaths by NHS region
lag_cor_reg <- data.frame()
for (i in 0:30) {
summary <-
all_data %>%
group_by(nhs_region) %>%
mutate(note_lag = lag(count, i)) %>%
## calculate rank correlation and bootstrap CI for each region
group_modify(~getboot(.x)) %>%
mutate(lag = i)
lag_cor_reg <- bind_rows(lag_cor_reg, summary)
}
cor_vs_lag_reg <-
lag_cor_reg %>%
ggplot(aes(lag, r, col = nhs_region)) +
geom_hline(yintercept = 0, lty = "longdash") +
geom_ribbon(aes(ymin = r_low, ymax = r_hi, col = NULL, fill = nhs_region), alpha = 0.2) +
geom_point() +
geom_line() +
facet_wrap(~nhs_region) +
scale_color_manual(values = pal) +
scale_fill_manual(values = pal, guide = F) +
theme_bw() +
labs(x = "Lag between NHS pathways and death data (days)", y = "Pearson's correlation", col = "NHS region") +
theme(legend.position = "bottom") +
guides(color = guide_legend(override.aes = list(fill = NA)))
cor_vs_lag_reg
5 Export data
We save the tables created during our analysis:
if (!dir.exists("excel_tables")) {
dir.create("excel_tables")
}
## list all tables, and loop over export
tables_to_export <- c("r_all_sliding", "lag_cor")
for (e in tables_to_export) {
rio::export(get(e),
file.path("excel_tables",
paste0(e, ".xlsx")))
}
## also export result from regression on lagged data
rio::export(lag_mod, file.path("excel_tables", "lag_mod.rds"))6 System information
6.1 Outline
The following information documents the system on which the document was compiled.
6.2 System
This provides information on the operating system.
6.3 R environment
This provides information on the version of R used:
6.4 R packages
This provides information on the packages used:
sessionInfo()
## R version 3.6.3 (2020-02-29)
## Platform: x86_64-apple-darwin15.6.0 (64-bit)
## Running under: macOS Catalina 10.15.5
##
## Matrix products: default
## BLAS: /Library/Frameworks/R.framework/Versions/3.6/Resources/lib/libRblas.0.dylib
## LAPACK: /Library/Frameworks/R.framework/Versions/3.6/Resources/lib/libRlapack.dylib
##
## locale:
## [1] en_US.UTF-8/en_US.UTF-8/en_US.UTF-8/C/en_US.UTF-8/en_US.UTF-8
##
## attached base packages:
## [1] stats graphics grDevices utils datasets methods base
##
## other attached packages:
## [1] ggnewscale_0.4.1 ggpubr_0.3.0 lubridate_1.7.8
## [4] chngpt_2020.5-21 cyphr_1.1.0 DT_0.13
## [7] kableExtra_1.1.0 janitor_2.0.1 remotes_2.1.1
## [10] projections_0.4.1 earlyR_0.0.1 epitrix_0.2.2
## [13] distcrete_1.0.3 incidence_1.7.1 rio_0.5.16
## [16] reshape2_1.4.4 rvest_0.3.5 xml2_1.3.2
## [19] linelist_0.0.40.9000 forcats_0.5.0 stringr_1.4.0
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##
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